{
  "id": "2310.02808",
  "version": "v1",
  "published": "2023-10-04T13:35:13.000Z",
  "updated": "2023-10-04T13:35:13.000Z",
  "title": "Probabilistic Method to Fundamental gap problems on the sphere",
  "authors": [
    "Gunhee Cho",
    "Guofang Wei",
    "Guang Yang"
  ],
  "categories": [
    "math.PR",
    "math.DG"
  ],
  "abstract": "We provide a probabilistic proof of the fundamental gap estimate for Schr\\\"odinger operators in convex domains on the sphere, which extends the probabilistic proof of F. Gong, H. Li, and D. Luo for the Euclidean case. Our results further generalize the results achieved for the Laplacian by S. Seto, L. Wang, and G. Wei, as well as by C. He, G. Wei, and Qi S. Zhang. The essential ingredient in our analysis is the reflection coupling method on Riemannian manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-04T13:35:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fundamental gap problems",
      "probabilistic method",
      "probabilistic proof",
      "fundamental gap estimate",
      "convex domains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}